Correct Answer - Option 2 :

\(K=\dfrac{4EI}{L}\)

__Explanation__

Stiffness (k) is defined as the force per unit deflection or moment required per unit rotation.

Stiffness factor for a beam simply supported at both ends is 3EI/L

__Important Points:__

For the far end being Hinged Supported:

If a unit rotation is to be caused at an end A for the far end being hinged support. Moment of \(\frac{{3EI}}{L}\) is to be applied at end and hence stiffness for the member is said to be \(\frac{{3EI}}{L}.\)

For the far end being Fixed Supported:

If a unit rotation is to be caused at an end A for the far end being fixed supported. Moment of \(\frac{{4EI}}{L}\) is to be applied at end and hence stiffness for the member is said to be \(\frac{{4EI}}{L}.\)